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Stable standing waves for the two-dimensional Klein–Gordon–Schrödinger system

Published online by Cambridge University Press:  01 October 2010

Hiroaki Kikuchi
Hiroaki Kikuchi
Affiliation:
Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan ([email protected])
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Abstract

We study the orbital stability of standing waves for the Klein–Gordon–Schrödinger system in two spatial dimensions. It is proved that the standing wave is stable if the frequency is sufficiently small. To prove this, we obtain the uniqueness of ground state and investigate the spectrum of the appropriate linearized operator by using the perturbation method developed by Genoud and Stuart and Lin and Wei. Then we apply to our system the general theory of Grillakis, Shatah and Strauss.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 140 , Issue 5 , October 2010 , pp. 1011 - 1039
Copyright
Copyright © Royal Society of Edinburgh 2010

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